Cell　deformation　and　adhesion　under　shear　flows　play　an　important　role　in　both　cell　migration　in　vivo　and　capture　based　microfluidic　devices　in　vitro.　Adhesion　dynamics　of　captured　cell　(e.g.,　firm　adhesion,　cell　rolling　and　cell　detachment)　under　steady　shear　flows　have　been　studied　extensively.　However,　cell　adhesion　under　accelerating　flows　is　common　both　in　vivo　and　in　vitro,　and　dynamics　of　cell　adhesion　under　accelerating　flows　remains　unknown.　As　such,　we　used　a　mathematical　model　based　on　the　front　tracking　method　and　investigated　the　effect　of　flow　acceleration　on　deformation　and　adhesion　dynamics　of　captured　cells,　including　cell　deformation　index,　cell　shape　evolution,　the　velocities　of　cell　center,　contact　time　and　wall　shear　stress　for　cell　rolling　and　detachment　by　using　a　series　of　parameter　values　for　leukocyte.　The　results　showed　that　the　cell　presented　three　dynamics　states　(i.e.,　firm　adhesion,　rolling　and　detachment)　with　increasing　wall　shear　stress　under　uniform　flows.　Wall　shear　stresses　were　＜　0.56　Pa　and　＞　1.12　Pa　for　firm　adhesion　and　detachment,　respectively.　The　wall　shear　stresses　were　at　the　range　1.48-1.63　Pa　(higher　than　1.12　Pa)　when　cell　left　the　bottom　surface　of　the　channel　under　flow　accelerations　(a　=　0.975-1.625　m/s(2)).　The　minimum　of　deformation　index　under　accelerating　flow　was　smaller　than　that　under　uniform　flow.　In　conclusion,　the　flow　acceleration　promotes　the　deformation　and　adhesion　of　captured　cells.　These　findings　could　further　the　understanding　of　cell　migration　in　vivo　and　promote　the　development　of　capture　based　microfluidic　devices　in　vitro.